Question

How do I solve for x and y?

Answer 1

x = 80

y = 160

Explanation:

The sum of all arc measures that make up a circle is 360°. Therefore:

`\implies 200^(\circ) + y^(\circ) = 360^(\circ)`

`\implies 200^(\circ) + y^(\circ) - 200^(\circ) = 360^(\circ) - 200^(\circ)`

`\implies y^(\circ) = 160^(\circ)`

`\implies y=160`

Tangent and Intersected Chord Theorem

If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one-half the measure of its intercepted arc.

Therefore, according to the Tangent and Intersected Chord Theorem, the measure of angle x is equal to half of the measure of arc y:

`\implies x^(\circ)=(1)/(2) y^(\circ)`

`\implies x^(\circ)=(1)/(2) \cdot 160^(\circ)`

`\implies x^(\circ)=80^(\circ)`

`\implies x=80`

`\hrulefill`

Circle Theorem vocabulary

• Chord: A straight line joining two points on the circle.
• Tangent: A straight line that touches a circle at only one point.
• Arc: the curve between two points on the circumference of a circle
• Intercepted arc: The curve between the points where two chords or line segments intercept the circumference of a circle.